The decrease in amplitude from one cycle to the next depends on the extent of damping in the system. The successive peak amplitudes bear a certain specific relationship involving the damping of the system, leading us to the concept of "logarithmic decrement" which we will now discuss.
It is often necessary to estimate the extent of damping present in a given system. Essentially the experimental techniques to determine damping in a system fall into two categories -- those based on free vibration tests and secondly those based on forced vibration tests. The latter require more sophisticated equipment/instruments, while the former is a relatively simple test. In a free vibration test, based on the measured peak amplitudes over several cycles (and thus estimating the "logarithmic decrement"), one can readily find the damping factor for the given system. We will now discuss these aspects. |
< 1”, x(t) is a damped sinusoid and the system exhibits a vibratory motion whose amplitude keeps diminishing as shown in fig 10.3.1. This is the most common vibration case and we will spend most of our time studying such systems. These are referred to as 
